A leading doctor-appointment scheduling app company wants to make "Unsick Days" the norm in the United States. It's encouraging employers to give their workers an extra paid day off during the year, so that they can get preventative care checkups without worrying about job repercussions.

In doing so, says the CEO of Zocdoc, companies will make sure the billions of dollars they spend contributing to employees' health-care plans each year are put to good use by paying for visits that could keep them in better health — and possibly preventing workers from having to take a sick day or two.

Zocdoc's push for Unsick Days cites a new survey that it sponsored, which found that half of workers said either their employer or workplace culture makes them feel they shouldn't schedule annual physicals, teeth cleaning and other preventative appointments during their work hours.

Some 60 percent of workers said they feel uncomfortable taking time off from work to go to those appointments. About 50 percent said if they miss work for preventative care appointments, they're worried it will harm their chances of getting a promotion, according to the survey, which was conduced with Kelton Global.

Kharraz noted his company, whose business model relies on patients scheduling doctor appointments, isn't immune from that conflict between health and work. In conducting the survey, Zocdoc found that only about one-third of its workers were using all of the preventative services covered by their health plan.

"It was really shocking to me to see that, because we're a health-care company," Kharraz said.

Creating a specific day to get preventative care while getting paid, he said, is a way to get over the hangups that workers and bosses might have about booking appointments during the workday.

"There needs to be explicit permission for employees to go there," Kharraz said.

So far, Zocdoc has partnered with 11 other companies, including Virgin Hotels, Foursquare, Zola wedding registry, Handy and the Oscar health insurance company to agree to offer an Unsick Day to their employees.

As part of the program, companies can either add an extra day to a worker's allotment of paid days off — which is the recommended option — or encourage them to use an existing paid day off to get preventative care.

Kharraz said there is good reason that others will sign up once the concept becomes widely known.

"There's already a general realization ... that healthy employees are more productive employees," he said, pointing to the proliferation of wellness programs in corporate America, and the continued willingness of companies to pay for the health plan benefits for workers.

But if workers feel inhibited about going to the doctor because of workplace pressure, "these [health] benefits got unused, and you're wasting millions of dollars."

Unsick Days, he said, "is another example where an ounce of prevention is worth a pound of cure."